Approximate Diagonalization of Homomorphisms from AH-Algebras to Certain Simple Classifiable C*-Algebras

TL;DR

This paper proves that unital homomorphisms from continuous functions on compact spaces to matrices over certain simple C*-algebras are approximately diagonalizable, with some generalizations explored.

Contribution

It establishes approximate diagonalization results for homomorphisms into C*-algebras with low tracial rank, extending previous understanding.

Findings

Unital homomorphisms are approximately diagonalizable in the specified setting.

Generalizations of the main result are provided.

The work advances classification techniques for C*-algebras.

Abstract

In this paper, we prove that unital homomorphisms from continuous functions on a compact metric space to matrices over a C*-algebra with tracial rank at most one are approximately diagonalizable. We also consider some generalizations of this result.